Question 11 and 12, Exercise 6.3
Solutions of Question 11 and 12 of Exercise 6.3 of Unit 06: Permutation and Combination. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan.
Question 11
Number of diagonals in n-sided polygon is 35. Find the number n?
Solution.
So given that nC2−n=35orn!2!(n−2)!−n=35n(n−1)(n−2)!2(n−2)!−n=35n(n−1)−2n2=35n2−n−2n=70n2−3n−70=0n2+7n−10n−70=0n(n+7)−10(n+7)=0(n+7)(n−10)=0n+7=0 or n−10=0n=−7n=10 n can not be negative, so n=10
Question 12
For the post of 6 officers, there are 100 appliciants,
2 posts are reserved for serving candidiates and remaining for others.
There are 20 serving candidates among the appliciants. In how many ways this selection can be made?
Solution.
2 candidate would be chosen out of 20 applications of serving candidates
and 4 candidates would be chosen out of remaining 80 applicants.
Possible ways of selection
=20C2×80C4=190×1581580=300500200
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